2,629 research outputs found
IMPROVING THE UNIVERSITY'S PERFORMANCE IN PUBLIC POLICY EDUCATION
Teaching/Communication/Extension/Profession,
Rectification of a whole-sky photograph as a tool for determining spatial positioning of cumulus clouds
There are no author-identified significant results in this report
-confidence sets in high-dimensional regression
We study a high-dimensional regression model. Aim is to construct a
confidence set for a given group of regression coefficients, treating all other
regression coefficients as nuisance parameters. We apply a one-step procedure
with the square-root Lasso as initial estimator and a multivariate square-root
Lasso for constructing a surrogate Fisher information matrix. The multivariate
square-root Lasso is based on nuclear norm loss with -penalty. We show
that this procedure leads to an asymptotically -distributed pivot, with
a remainder term depending only on the -error of the initial estimator.
We show that under -sparsity conditions on the regression coefficients
the square-root Lasso produces to a consistent estimator of the noise
variance and we establish sharp oracle inequalities which show that the
remainder term is small under further sparsity conditions on and
compatibility conditions on the design.Comment: 22 page
Sharp Oracle Inequalities for Square Root Regularization
We study a set of regularization methods for high-dimensional linear
regression models. These penalized estimators have the square root of the
residual sum of squared errors as loss function, and any weakly decomposable
norm as penalty function. This fit measure is chosen because of its property
that the estimator does not depend on the unknown standard deviation of the
noise. On the other hand, a generalized weakly decomposable norm penalty is
very useful in being able to deal with different underlying sparsity
structures. We can choose a different sparsity inducing norm depending on how
we want to interpret the unknown parameter vector . Structured sparsity
norms, as defined in Micchelli et al. [18], are special cases of weakly
decomposable norms, therefore we also include the square root LASSO (Belloni et
al. [3]), the group square root LASSO (Bunea et al. [10]) and a new method
called the square root SLOPE (in a similar fashion to the SLOPE from Bogdan et
al. [6]). For this collection of estimators our results provide sharp oracle
inequalities with the Karush-Kuhn-Tucker conditions. We discuss some examples
of estimators. Based on a simulation we illustrate some advantages of the
square root SLOPE
A remark on nets of threshold elements
The necessary condition for transition functions of Simple McCulloch-Pitts Nets, given in the article: “Nets of Threshold Elements≓ by Kenneth Krohn and John Rhodes in Corollary 3.1. (iii) is enlarged to a sufficient criterion by addition of another necessary condition
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Morphology, Bioacoustics, and Ecology of Tibicen neomexicensis sp. n., a New Species of cicada from the Sacramento Mountains in New Mexico, U.S.A. (Hemiptera, Cicadidae, Tibicen)
Tibicen neomexicensis sp. n., a new species of cicada found in the Sacramento Mountains of southcentral New Mexico, is described. T. neomexicensis closely resembles T. chiricahua Davis morphologically, but males of the two species have highly distinct calling songs that differ in phrasal structure, amplitude burst rates, and pulse structure. Unlike T. chiricahua, male T. neomexicensis use conspicuous dorso-ventral abdominal movements to modulate the amplitude and frequency of their calls. T. neomexicensis is also smaller on average than T. chiricahua, and differences in the color patterns of the wing venation identify these two species morphologically. Both species are dependent on pinyon-juniper woodlands and have similar emergence phenologies. These species appear to be allopatric, with T. chiricahua found west of the Rio Grande in New Mexico, Arizona, and Mexico, and T. neomexicensis so far known only from New Mexico, east of the Rio Grande. T. chiricahua and T. neomexicensis males share a common genitalic structure that separates them from all other species of Tibicen, and the possible evolutionary and biogeographic history of these likely sister species is also discussed
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